48 
Proceedings of the Royal Society of Edinburgh. [Sess. 
with the wave-length, until JcL equals perhaps 671 -, or X = JL, but to all 
further diminutions of X it should remain constant. J. J. Thomson’s 
formula offers an irreducible minimum. There appears to be no way of 
getting below it except by reducing the number of scattering electrons, 
i.e. by making this less than the atomic number. So the question must 
be left open at present. Apart from this difficulty, formula (3) seems to 
be useful in explaining the scattering of y-rays. The curves on p. 281 of 
Rutherford’s Radioactive Substances and their Radiations are not unlike 
those in fig. 4. 
If the atoms in aluminium were arranged cubically, they would be 
2‘56 x 10“ 8 cm. apart. J. J. Thomson’s formula gives about T9 for the 
mass-scattering coefficient of aluminium. This is the experimental value 
for \ = T66xlO" 8 cm. Consequently the average value of L should be 
about 3 x T66 x 10 _8 = , 5 X 10 -8 cm. Thus if there are thirteen electrons in 
the aluminium atom, there is quite sufficient space to get them all in. 
J. J. Thomson’s theory of scattering is inconsistent with the Bohr 
atom model. For, according to the latter, the electrons revolve in rings, 
yet in defiance of all the laws of electromagnetism the acceleration 
necessary to keep them in their orbits is unaccompanied by radiation. 
But according to the theory of scattering the acceleration produced by 
the light wave is accompanied by radiation. We cannot, without further 
explanation, maintain at the same time that acceleration is and is not 
accompanied by radiation. 
§ 4. J. J. Thomson’s theory of scattering was written before the nature 
of X-rays was ascertained, and he assumes that they consist of short, sharp 
pulses.* We know now that they consist of harmonic trains distinguished 
only from ordinary light by their extremely short wave-length. It is con- 
sequently necessary to examine the derivation of the formula afresh. 
* Conduction of Electricity through Gases , p. 269. 
